Ghost story. II. The midpoint ghost vertex

Understand

We construct the ghost number 9 three strings vertex for OSFT in the natural normal ordering.

• We find two versions, one with a ghost insertion at z=i and a twist-conjugate one with insertion at z=-i.
• For this reason we call them midpoint vertices.
• We show that the relevant Neumann matrices commute among themselves and with the matrix $G$ representing the operator K1.